Time: Tuesday, Oct 25, 2016, 2:00pm @ MTH1311

Speaker: Prof. Greg Coxson (United States Naval Acadamy)

Title: Enumeration and Generation of Binary and Quad-Phase Code PSL Equivalence Classes

Abstract: The problem of optimizing binary and quad-phase aperiodic autocorrelation sidelobe levels is notoriously difficult, and likely NP-hard. Some have likened these problems to that of seeking needles in a haystack. I have at times tried to find aspects of these problems that can be used to predict behavior for all code lengths N, but these efforts have always ended in frustration. However, recently, I posed a question about the binary case that not only yielded an enumeration result for all code lengths N, but even led to a similar result for the quad-phase case. A side benefit of the work is a pair of simple algorithms for visiting, one-by-one, single representatives of each PSL equivalence class for any code length N of interest. Such algorithms can be employed, ideally in combination with other methods, to expedite searches for low-sidelobe binary and quad-phase codes. Interestingly, this process has also caused me to learn some of the Basque language, and even some elements of the Theories of Knots and Braids. I hope to find a way to work the associated stories into my talk. Back to seminar